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We summarize the known obstructions to subfactors with principal graphs which begin with a triple point.
Index for subfactors
Vaughan F. R. Jones · 1983
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Quantized groups, string algebras and Galois theory for algebras
Adrian Ocneanu · 1988
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Coxeter graphs and towers of algebras
Frederick M. Goodman, Pierre de la Harpe, and Vaughan F. R. Jones · 1989
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A survey on spectra of infinite graphs
Bojan Mohar and Wolfgang Woess · 1989
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Markov traces on universal Jones algebras and subfactors of finite index
Sorin Popa · 1993
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Principal graphs of subfactors in the index range 4 < [ M : N ] < 3 + 2 4<[M:N]<3+\sqrt{2}
Uffe Haagerup · 1994
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Classification of amenable subfactors of type II
Sorin Popa · 1994
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An axiomatization of the lattice of higher relative commutants of a subfactor
Sorin Popa · 1995
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Algebras associated to intermediate subfactors
Dietmar Bisch and Vaughan Jones · 1997
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Principal graphs of subfactors with small Jones index
Dietmar Bisch · 1998
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Quantum symmetries on operator algebras
David E. Evans and Yasuyuki Kawahigashi · 1998
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The representation theory of affine Temperley-Lieb algebras
John J. Graham and Gus I. Lehrer · 1998
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Exotic subfactors of finite depth with Jones indices ( 5 + 13 ) / 2 (5+\sqrt{13})/2 and ( 5 + 17 ) / 2 (5+\sqrt{17})/2
Marta Asaeda and Uffe Haagerup · 1999
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The structure of sectors associated with Longo-Rehren inclusions. II. Examples
Masaki Izumi · 2001
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Quadratic tangles in planar algebras, 2003
Vaughan F. R. Jones · 2003
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On Haagerup’s list of potential principal graphs of subfactors
Marta Asaeda and Seidai Yasuda · 2009
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Constructing the extended Haagerup planar algebra, 2009
Stephen Bigelow, Scott Morrison, Emily Peters, and Noah Snyder · 2009
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A planar algebra construction of the Haagerup subfactor, 2009
Emily Peters · 2009
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Cyclotomic integers, fusion categories, and subfactors, 2010
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The annular structure of subfactors
Vaughan F. R. Jones · 2001
Cited alongside, same era.
The graph planar algebra embedding theorem
Scott Morrison and Kevin Walker
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Frank Calegari, Scott Morrison, and Noah Snyder · 2010
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Subfactors of index less than 5, part 1: the principal graph odometer, 2010
Scott Morrison and Noah Snyder · 2010
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Classification of subfactors of index less than 5, part 4: cyclotomicity, 2010
David Penneys and James Tener · 2010
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